The big four slipped further into deflationary territory this month as Sainsbury’s followed rivals in slashing prices on a number of known value items.

Average annual inflation as measured by The Grocer Price Index edged into negative territory last month, at -0.01%, and this month has fallen again, to -0.26%.

Inflation rates are now broadly similar across the supermarkets. At Asda and Tesco, inflation is running at -0.01% and 0% respectively, while at Sainsbury’s and Morrisons prices are down year on year by 0.83% and 0.23%. Only Waitrose remains in positive territory with prices 0.55% higher than a year ago.

However, on a month on month basis, it is Waitrose that has seen the biggest fall in price, followed by Sainsbury’s. Waitrose has slashed prices 1.88% over the past month, with cuts evenly spread across a broad range of categories. Prices fell in all the 14 categories tracked by the GPI bar the smallest - deli.

Sainsbury’s prices have fallen 1.14% month on month. It has cut prices by 2% or more across health & beauty, household, deli, frozen and baby, but the biggest cuts were in fruit and vegetables, where prices fell 5.67%.

Sainsbury’s followed Tesco and Morrisons in cutting the price of key produce lines, including carrots, broccoli, iceberg lettuce and courgettes. The cuts come after it reduced the price of other big-selling own-label lines, including butter and eggs, at the end of April.

As a result of the price-cutting across the supermarkets on fruit & veg, average category prices are now 4% down on last year.

The other category that has seen a big shift in recent months is meat, fish and poultry. Inflation in the category was running at more than 7% last summer in the wake of the horsemeat scandal, but has now plummeted to 1.72%. alcohol inflation has also dropped significantly, falling steadily from close to 4% a year ago to -0.64%.

The falling cost of key commodities like wheat, corn and sugar has helped take the heat out of inflation. Inflation eased through the second half of last year, long before the start of the supermarket price war. But the price-cutting of recent months has put further downward pressure on pricing.

This week’s guest editor Chris Bush said Tesco was partly responsible for the current deflationary environment.

“The lead we took has definitely created a response in the industry,” he said.

“Certainly when you look at the investments on everyday items, a lot of deflation has come from there.”

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